Figure out how to maximize profit by solving linear programming problems graphically
I'm new to this site so I'm hoping this is the right area to post this. I'm dealing with a finite mathematics problem. Okay so my professor made up a bunch of problems only thing is they are very different from the ones in our book so I'm not as sure how to go about them. The problem reads:
I need to be able to:
- A small country grows only 2 crops for export:coffee and cocoa. The country has 500,000 hectares of land available for the crops. Long term contracts require that at least 100,000 hectares of land be devoted to coffee and at least 200,000 hectares to cocoa. Cocoa must be processed locally and production conditions limit cocoa to 270,000 hectares. Coffee requires 2 workers per hectare and cocoa requires 5 workers per hectare. No more than 1,750,000 people are available for working these crops. Coffee produces a profit of $220 per hectare and cocoa a profit of $550 per hectare. How many hectares should the country devote to each crop in order to maximize profit?
Can anyone help me figure this out without just giving me the answer , kinda like help me out step by step?Thanks.
- clearly define the two variables
- determine the system of constraints that models the situation.
- determine the objective function for the situation
- Graph and shade the feasible solutions region (which i think i can handle if i had the right system of constraints)
- Evaluate the objective function for each of the corner points. (have serious problems with)
- Determine the values of the variables that will optimize the objective function.
problem with objective function i think
thanks. I think my problem is still in the constraints and objective function. When I set it up I use A=Coffee, B=cocoa:
A greater then or equal to 100,000
B greater then or equal to 200,000
B less then or equal to 270,000
2A+5B less then or equal to 1,750,000
A greater than or equal to 0
B greater than or equal to 0
(but to me this part doesnt sound right because i added in another variable P=profit)
Any clue as to where I'm going wrong?